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<H3>pair_style coul/cut command 
</H3>
<H3>pair_style coul/cut/omp command 
</H3>
<H3>pair_style coul/debye command 
</H3>
<H3>pair_style coul/debye/omp command 
</H3>
<H3>pair_style coul/dsf command 
</H3>
<H3>pair_style coul/dsf/gpu command 
</H3>
<H3>pair_style coul/long command 
</H3>
<H3>pair_style coul/long/omp command 
</H3>
<H3>pair_style coul/long/gpu command 
</H3>
<H3>pair_style coul/msm command 
</H3>
<H3>pair_style coul/msm/omp command 
</H3>
<H3>pair_style coul/wolf command 
</H3>
<H3>pair_style coul/wolf/omp command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style coul/cut cutoff
pair_style coul/debye kappa cutoff
pair_style coul/dsf alpha cutoff
pair_style coul/long cutoff
pair_style coul/long/gpu cutoff 
pair_style coul/wolf alpha cutoff 
</PRE>
<UL><LI>cutoff = global cutoff for Coulombic interactions
<LI>kappa = Debye length (inverse distance units) 
<LI>alpha = damping parameter (inverse distance units) 
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style coul/cut 2.5
pair_coeff * *
pair_coeff 2 2 3.5 
</PRE>
<PRE>pair_style coul/debye 1.4 3.0
pair_coeff * *
pair_coeff 2 2 3.5 
</PRE>
<PRE>pair_style coul/dsf 0.05 10.0
pair_coeff * * 
</PRE>
<PRE>pair_style coul/long 10.0
pair_coeff * * 
</PRE>
<PRE>pair_style coul/msm 10.0
pair_coeff * * 
</PRE>
<PRE>pair_style coul/wolf 0.2 9.0
pair_coeff * * 
</PRE>
<P><B>Description:</B>
</P>
<P>The <I>coul/cut</I> style computes the standard Coulombic interaction
potential given by
</P>
<CENTER><IMG SRC = "Eqs/pair_coulomb.jpg">
</CENTER>
<P>where C is an energy-conversion constant, Qi and Qj are the charges on
the 2 atoms, and epsilon is the dielectric constant which can be set
by the <A HREF = "dielectric.html">dielectric</A> command.  The cutoff Rc truncates
the interaction distance.
</P>
<P>Style <I>coul/debye</I> adds an additional exp() damping factor to the
Coulombic term, given by
</P>
<CENTER><IMG SRC = "Eqs/pair_debye.jpg">
</CENTER>
<P>where kappa is the Debye length.  This potential is another way to
mimic the screening effect of a polar solvent.
</P>
<P>Style <I>coul/dsf</I> computes Coulombic interactions via the damped 
shifted force model described in <A HREF = "#Fennell">Fennell</A>, given by:
</P>
<CENTER><IMG SRC = "Eqs/pair_coul_dsf.jpg">
</CENTER>
<P>where <I>alpha</I> is the damping parameter and erfc() is the
complementary error-function. The potential corrects issues in the
Wolf model (described below) to provide consistent forces and energies
(the Wolf potential is not differentiable at the cutoff) and smooth
decay to zero.
</P>
<P>Style <I>coul/wolf</I> computes Coulombic interactions via the Wolf
summation method, described in <A HREF = "#Wolf">Wolf</A>, given by:
</P>
<CENTER><IMG SRC = "Eqs/pair_coul_wolf.jpg">
</CENTER>
<P>where <I>alpha</I> is the damping parameter, and erc() and erfc() are
error-fuction and complementary error-function terms.  This potential
is essentially a short-range, spherically-truncated,
charge-neutralized, shifted, pairwise <I>1/r</I> summation.  With a
manipulation of adding and substracting a self term (for i = j) to the
first and second term on the right-hand-side, respectively, and a
small enough <I>alpha</I> damping parameter, the second term shrinks and
the potential becomes a rapidly-converging real-space summation.  With
a long enough cutoff and small enough alpha parameter, the energy and
forces calcluated by the Wolf summation method approach those of the
Ewald sum.  So it is a means of getting effective long-range
interactions with a short-range potential.
</P>
<P>Styles <I>coul/long</I> and <I>coul/msm</I> compute the same Coulombic
interactions as style <I>coul/cut</I> except that an additional damping
factor is applied so it can be used in conjunction with the
<A HREF = "kspace_style.html">kspace_style</A> command and its <I>ewald</I> or <I>pppm</I>
option.  The Coulombic cutoff specified for this style means that
pairwise interactions within this distance are computed directly;
interactions outside that distance are computed in reciprocal space.
</P>
<P>These potentials are designed to be combined with other pair
potentials via the <A HREF = "pair_hybrid.html">pair_style hybrid/overlay</A>
command.  This is because they have no repulsive core.  Hence if they
are used by themselves, there will be no repulsion to keep two
oppositely charged particles from overlapping each other.
</P>
<P>The following coefficients must be defined for each pair of atoms
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands, or by mixing as described below:
</P>
<UL><LI>cutoff (distance units) 
</UL>
<P>For <I>coul/cut</I> and <I>coul/debye</I>, the cutoff coefficient is optional.
If it is not used (as in some of the examples above), the default
global value specified in the pair_style command is used.
</P>
<P>For <I>coul/long</I> and <I>coul/msm</I> no cutoff can be specified for an
individual I,J type pair via the pair_coeff command.  All type pairs
use the same global Coulombic cutoff specified in the pair_style
command.
</P>
<HR>

<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>omp</I>, or <I>opt</I> suffix are functionally
the same as the corresponding style without the suffix.  They have
been optimized to run faster, depending on your available hardware, as
discussed in <A HREF = "Section_accelerate.html">Section_accelerate</A> of the
manual.  The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.
</P>
<P>These accelerated styles are part of the USER-CUDA, GPU, USER-OMP and OPT
packages, respectively.  They are only enabled if LAMMPS was built with
those packages.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info.
</P>
<P>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
switch</A> when you invoke LAMMPS, or you can
use the <A HREF = "suffix.html">suffix</A> command in your input script.
</P>
<P>See <A HREF = "Section_accelerate.html">Section_accelerate</A> of the manual for
more instructions on how to use the accelerated styles effectively.
</P>
<HR>

<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
</P>
<P>For atom type pairs I,J and I != J, the cutoff distance for the
<I>coul/cut</I> style can be mixed.  The default mix value is <I>geometric</I>.
See the "pair_modify" command for details.
</P>
<P>The <A HREF = "pair_modify.html">pair_modify</A> shift option is not relevant
for these pair styles.
</P>
<P>The <I>coul/long</I> style supports the <A HREF = "pair_modify.html">pair_modify</A>
table option for tabulation of the short-range portion of the
long-range Coulombic interaction.
</P>
<P>These pair styles do not support the <A HREF = "pair_modify.html">pair_modify</A>
tail option for adding long-range tail corrections to energy and
pressure.
</P>
<P>These pair styles write their information to <A HREF = "restart.html">binary restart
files</A>, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.
</P>
<P>This pair style can only be used via the <I>pair</I> keyword of the
<A HREF = "run_style.html">run_style respa</A> command.  It does not support the
<I>inner</I>, <I>middle</I>, <I>outer</I> keywords.
</P>
<HR>

<P><B>Restrictions:</B>
</P>
<P>The <I>coul/long</I> style is part of the KSPACE package.  It is only
enabled if LAMMPS was built with that package (which it is by
default).  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A> section
for more info.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "pair_hybrid.html">pair_style
hybrid/overlay</A>
</P>
<P><B>Default:</B> none
</P>
<HR>

<A NAME = "Wolf"></A>

<P><B>(Wolf)</B> D. Wolf, P. Keblinski, S. R. Phillpot, J. Eggebrecht, J Chem
Phys, 110, 8254 (1999).
</P>
<A NAME = "Fennell"></A>

<P><B>(Fennell)</B> C. J. Fennell, J. D. Gezelter, J Chem Phys, 124, 
234104 (2006).
</P>
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